In the present work, we study analytically and numerically the influence of the thermal conductivity and the thickness of the walls of a horizontal rectangular cell on the species separation of binary mixture. This problem is of great importance for species separation by thermogravitational diffusion. The thickness of the fluid layer leading to optimal separation is less than a millimeter for the binary mixtures investigated and the wall thickness is of the order of two millimeters or more. Furthermore the conductivity of the plates is generally different from the conductivity of the saturated porous layer. We consider a horizontal cell of large longitudinal extension filled with a porous medium saturated by a binary mixture bounded by plates of the same thickness and the same thermal conductivity. The outer surfaces of plates are subjected to a constant heat flux. We study the stability of the equilibrium solution and the unicellular flow. The equilibrium solution is found to lose stability via a stationary bifurcation or a Hopf bifurcation depending on the values of the dimensionless parameters of the problem. For separation ratio ψ ≥ ψmono , the critical parameters associated to the primary transition are Racs = 12(1+2dδ)/(1+ψ(1+Le+2Le dδ)) and kcs = 0 which corresponds to the transition between the equilibrium solution and the unicellular one. In these relation Le is the Lewis number, δ is the ratio of plates over the porous layer thickness and d, their respective thermal conductivity ratio. A very good agreement is found between the critical values obtained analytically and the ones obtained by the spectral Tau numerical procedure.We show in this work that the separation of the species in binary mixtures depends strongly on d and δ for values of the Rayleigh number greater than the Rayleigh number leading to the maximum separation. It also emerges from this study that the separation is underestimated when we do not take into account the effect of the conducting walls. A good agreement is observed between the analytical results and the numerical simulations. In the last part of the thesis, we undertake experimental work on the separation in nanofluids containing nanotubes of carbon.
